The second itinerary, the shorter by distance, appears to be the only correct one. Rome2Rio apparently has a little bug, confusing Santa Elena, Mexico and Santa Elena, Guatemala, near Flores, as shown on the Linea Dora website. So only the second option is valid.
Looking at the itinerary on a map, this option looks not only the shortest in distance but probably also in duration, because it follows the main roads. There are 3 big cities crossed, Flores, Guatemala, Belize City and Chetumal, Mexico.
According to Rome2Rio it will take you 28 hours, but I could not find such an estimation on any other website (so it might not be correct). Google Maps predicts a drive of 15 hours to cover the 1100 km by car (without breaks), so the bus time is realistic, even if it does not stop anywhere else than the 3 big cities.
For the part from Guatemala City (on 17th street) to Belize City, you can use the services of the Fuente del Norte. It will cost you about 50-55$ (I suppose USD) according to the Linea Dora website. There are 5 to 10 buses per day including 2 by night. It might take you 10 hours to reach Santa Elena/Flores, Guatemala. Then several other hours (probably <5 because the bus going back leaves aat 10AM) to reach Belize City. Be careful there is only one daily bus and it leaves at 5AM so if you do not want to stop there, ask in Guatemala City what bus will get you there on time. Unlike what Rome2Rio announces, you will likely have a connection in Belize City.
Then from Belize City it seems you will take a Mexican carrier, ADO. The itinerary is not clear on their own website, but it is vaguely referenced in many places. In theory, you should connect in Chetumal, Mexico before reaching Cancun. The trip should be around 50 $ and take 10 to 15 hours (thebusschedule and Rome2Rio expect 6 hours, and there are frequent buses, about every half-hour to one and a half-hour between each bus)
So in the end you have only one option for a "reasonably short" trip - given the distance. It might take you about 30 hours depending on when you can catch a connection - you should have max 3 connections.